The standing vertical jump is a good test of an athlete's strength and fitness. The athlete goes into a deep crouch, then extends his legs rapidly; when his legs are fully extended, he leaves the ground and rises to his highest height. It is the force of the ground on the athlete during the extension phase that accelerates the athlete to the final speed with which he leaves the ground. A good jumper can exert a force on the ground equal to twice his weight. If his crouch is 55 cm deep, how far off the ground does he rise?

The athlete will rise 1.10 meters off the ground

Explanation:

Vertical Motion

If an object is launched vertically upwards at an initial speed vo, then it will reach a maximum height given by

The athlete can exert a net force upwards equal to twice his weight. It makes him accelerate upwards at

The speed at the end of his push can be computed by

Replacing the value of a obtained above:

where y is the length of this crouch

This is the initial speed of this vertical launch, thus

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.